Categorification and correlation functions in conformal field theory

A modular tensor category provides the appropriate data for the construction of a three-dimensional topological field theory. We describe the following analogue for two-dimensional conformal field theories: a 2-category whose objects are symmetric special Frobenius algebras in a modular tensor category and whose morphisms are categories of bimodules. This 2-category provides sufficient ingredients for constructing all correlation functions of a two-dimensional rational conformal field theory. The bimodules have the physical interpretation of chiral data, boundary conditions, and topological defect lines of this theory.Comment: 16 pages, Invited contribution to the ICM 200

Conformal Field Theories, Graphs and Quantum Algebras

This article reviews some recent progress in our understanding of the structure of Rational Conformal Field Theories, based on ideas that originate for a large part in the work of A. Ocneanu. The consistency conditions that generalize modular invariance for a given RCFT in the presence of various types of boundary conditions --open, twisted-- are encoded in a system of integer multiplicities that form matrix representations of fusion-like algebras. These multiplicities are also the combinatorial data that enable one to construct an abstract ``quantum'' algebra, whose $6j$- and $3j$-symbols contain essential information on the Operator Product Algebra of the RCFT and are part of a cell system, subject to pentagonal identities. It looks quite plausible that the classification of a wide class of RCFT amounts to a classification of ``Weak $C^*$- Hopf algebras''.Comment: 23 pages, 12 figures, LateX. To appear in MATHPHYS ODYSSEY 2001 --Integrable Models and Beyond, ed. M. Kashiwara and T. Miwa, Progress in Math., Birkhauser. References and comments adde

Fermions in three-dimensional spinfoam quantum gravity

We study the coupling of massive fermions to the quantum mechanical dynamics of spacetime emerging from the spinfoam approach in three dimensions. We first recall the classical theory before constructing a spinfoam model of quantum gravity coupled to spinors. The technique used is based on a finite expansion in inverse fermion masses leading to the computation of the vacuum to vacuum transition amplitude of the theory. The path integral is derived as a sum over closed fermionic loops wrapping around the spinfoam. The effects of quantum torsion are realised as a modification of the intertwining operators assigned to the edges of the two-complex, in accordance with loop quantum gravity. The creation of non-trivial curvature is modelled by a modification of the pure gravity vertex amplitudes. The appendix contains a review of the geometrical and algebraic structures underlying the classical coupling of fermions to three dimensional gravity.Comment: 40 pages, 3 figures, version accepted for publication in GER

Common features between neoplastic and preneoplastic lesions of the biliary tract and the pancreas

The bile duct system and pancreas show many similarities due to their anatomical proximity and common embryological origin. Consequently, preneoplastic and neoplastic lesions of the bile duct and pancreas share analogies in terms of molecular, histological and pathophysiological features. Intraepithelial neoplasms are reported in biliary tract, as biliary intraepithelial neoplasm (BilIN), and in pancreas, as pancreatic intraepithelial neoplasm (PanIN). Both can evolve to invasive carcinomas, respectively cholangiocarcinoma (CCA) and pancreatic ductal adenocarcinoma (PDAC). Intraductal papillary neoplasms arise in biliary tract and pancreas. Intraductal papillary neoplasm of the biliary tract (IPNB) share common histologic and phenotypic features such as pancreatobiliary, gastric, intestinal and oncocytic types, and biological behavior with the pancreatic counterpart, the intraductal papillary mucinous neoplasm of the pancreas (IPMN). All these neoplastic lesions exhibit similar immunohistochemical phenotypes, suggesting a common carcinogenic process. Indeed, CCA and PDAC display similar clinic-pathological features as growth pattern, poor response to conventional chemotherapy and radiotherapy and, as a consequence, an unfavorable prognosis. The objective of this review is to discuss similarities and differences between the neoplastic lesions of the pancreas and biliary tract with potential implications on a common origin from similar stem/progenitor cells

HEP-2 CELL IMAGES FLUORESCENCE INTENSITY CLASSIFICATION TO DETERMINE POSITIVITY BASED ON NEURAL NETWORK AMIN

Nowadays, the recommended method for detection of anti-nuclear auto-antibodies is by using Indirect Immunofluorescence (IIF). The increasing of test demands on classification of Hep-2 cell images force the physicians to carry out the test faster, resulting bad quality results. IIF diagnosis requires estimating the fluorescence intensity of the serum and this will be observed. As there are subjective and inter/intra laboratory perception of the results, the development of computer-aided diagnosis (CAD) tools is used to support the decision. In this report, we propose the classification technique based on Artificial Neural Network (ANN) that can classify the Hep-2 cell images into 3 classes namely positive, negative and intermediate,specifically to determine the presence of antinuclear autoantibodies (ANA)